Predictive maintenance is a powerful tool for reducing costly interruptions in modern manufacturing. One of its challenges is proactively detecting rare machine failures, which impact equipment health and process stability despite their infrequency. This paper introduces a combined approach to predicting rare machine failures and monitoring process stability using statistical and technological techniques. Initially, a data augmentation method is used to handle imbalanced data. Then, three machine learning algorithms (gradient boosting, K-nearest neighbour, and logistic regression) are tested and compared for their performance in detecting rare machine failures. Furthermore, principal component analysis is used to establish multivariate control charts, specifically TPCA2 and Q charts, to monitor manufacturing processes and equipment behaviour. The proposed approach, tested with real-world data, has demonstrated effective results in predicting rare failures and in monitoring equipment behaviour. [Received: 28 May 2024; Accepted: 30 April 2025]